A Note on Classical Modal Relevant Algebras

R. Meyer and E. Mares [10] studied the logic CNR, a classical relevant logic with a modal connective. Such logic is of type S4. As it has been noted in [10], the addition of a modal operator in the language of classical relevant logic and the axioms φ ∧ ψ → (φ ∧ ψ) and (φ ∧ ψ) → ( φ ∧ ψ) do not necessarily produce theorems such that as (φ→ ψ) → φ → ψ or (♦φ→ ψ) → (φ→ ψ). These formulas are well known theorems of classical modal logic [9]. We will define here classical relevant algebras with a modal operator. We shall investigate some types of algebras